numerical solution of couette flow using crank nicolson technique (implicit method)

1. NUMERICAL SOLUTION OF COUETTE FLOW USING CRANK
NICOLSON TECHNIQUE
MANOJKUMAR MAURYA
M.E. 13906

2. DEFINATION
• It is a flow between two parallel plates in which the lower plate is at rest
while the upper plate is moving.
• The plates are considered to be infinitely long
• The flow field is driven by the shear stress exerted on fluid due to the
movement of the upper plate.

3. Analytic method

4. Crank Nicolson technique

5. Governing equation

7. Crank Nicolson technique, the finite difference
representation

8. • We get different equations as we apply this
equation at different grid points
• The order of the matrix depends upon the
number of grid points taken into consideration
• The matrix thus obtained is tridiagonal matrix
which is converted into bidiagonal form using
Thomas algorithm or Gauss elimination
method

9. Stability criteria

10. Representation of tridiagonal matrix

11. Thomas algorithm